Note that the BS detects the messages of two users via NOMA technique, i.e., the BS first detects the message of strong user 1 and then detects the message of weak user 2 with SIC [1]}, [2]}, [3]}.
As a result, the achievable rates of user 1 and 2 in group \(i\)  can be given by (REF ) and (REF ), respectively.
Substituting \(r_{i1}=d_{i1}/t_i\)  and
\(r_{i2}=d_{i2}/t_i\)  obtained from (REF ) into (REF ) and (REF ) yields
\(p_{i1}=a_{i1}B\left( 2^{\frac{d_{i1}+d_{i2}}{Bt_i}}-2^{\frac{d_{i2}}{Bt_i}}\right), p_{i2}=a_{i2}B \left( 2^{\frac{d_{i2}}{Bt_i}}-1\right),\!\! \) 
